arXiv subjects

Łukasz Brzozowski

Publications and source records attributed to Łukasz Brzozowski.

4 recordsLinked to original sources

arXiv2026

Generating Synthetic Citation Networks with Communities

Generating realistic synthetic citation, patent, or component dependency networks is essential for benchmarking community detection, graph visualisation, and network data mining algorithms. We present a systematic comparison of generators of directed graphs that are nearly acyclic and have a ground-truth community structure. We evaluate 12 methods across 7 real citation networks and 26 metrics. We propose the practice of reversing the directions of edges in static generators to break cycles and induce a citation-like flow, which markedly improves the performance of a degree-corrected Stochastic Block Model. Our methodological approach to evaluating community detection benchmarks distinguishes between endogenous and exogenous mesoscopic similarities, with the latter proving more important. This distinction reveals that high-parameter models gain much of their advantage by memorising planted community statistics, which limits their fidelity when the evaluation is blind to those labels. Finally, we introduce the Citation Seeder (CS) algorithm, an iterative generator grounded in the Price-Pareto model of citation networks, with interpretable parameters and O(N+E) generation. CS achieves competitive results against the best-performing baselines while using up to four orders of magnitude fewer parameters, providing an interpretable account of a network's structure and, on a temporal hold-out, extrapolating its future in-degree distribution more faithfully than descriptive baselines.

cs.SI↗

arXiv2026

The Price-Pareto growth model of networks with community structure

We introduce a new analytical framework for modelling degree sequences in individual communities of real-world networks, e.g., citations to papers in different fields. Our work is inspired by a recent modification of the Price's model, which assumes that citations are gained partly accidentally, and to some extent preferentially. Our work addresses the need to represent the heterogeneity of various scientific domains, as standard homogeneous models fail to capture the distinct growth ratios and citing cultures of different fields. Extending the model to networks with a community structure allows us to devise the analytical formulae for, amongst others, citation counts in each cluster and their inequality as described by the Gini index. We also show that a citation count distribution in each community tends to a Pareto type II distribution. Thanks to the derived model parameter estimators, the new model can be fitted to real citation and similar networks.

physics.soc-ph↗

arXiv2025

Clustering with minimum spanning trees: How good can it be?

Minimum spanning trees (MSTs) provide a convenient representation of datasets in numerous pattern recognition activities. Moreover, they are relatively fast to compute. In this paper, we quantify the extent to which they are meaningful in low-dimensional partitional data clustering tasks. By identifying the upper bounds for the agreement between the best (oracle) algorithm and the expert labels from a large battery of benchmark data, we discover that MST methods can be very competitive. Next, we review, study, extend, and generalise a few existing, state-of-the-art MST-based partitioning schemes. This leads to some new noteworthy approaches. Overall, the Genie and the information-theoretic methods often outperform the non-MST algorithms such as K-means, Gaussian mixtures, spectral clustering, Birch, density-based, and classical hierarchical agglomerative procedures. Nevertheless, we identify that there is still some room for improvement, and thus the development of novel algorithms is encouraged.

stat.ML↗

arXiv2023

Community detection in complex networks via node similarity, graph representation learning, and hierarchical clustering

Community detection is a critical challenge in analysing real graphs, including social, transportation, citation, cybersecurity, and many other networks. This article proposes three new, general, hierarchical frameworks to deal with this task. The introduced approach supports various linkage-based clustering algorithms, vertex proximity matrices, and graph representation learning models. We compare over a hundred module combinations on the Stochastic Block Model graphs and real-life datasets. We observe that our best pipelines (Wasserman-Faust and the mutual information-based PPMI proximity, as well as the deep learning-based DNGR representations) perform competitively to the state-of-the-art Leiden and Louvain algorithms. At the same time, unlike the latter, they remain hierarchical. Thus, they output a series of nested partitions of all possible cardinalities which are compatible with each other. This feature is crucial when the number of correct partitions is unknown in advance.

cs.SI↗